Simplify the following expression: $ q = \dfrac{-7}{10} - \dfrac{8y}{7y + 6} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7y + 6}{7y + 6}$ $ \dfrac{-7}{10} \times \dfrac{7y + 6}{7y + 6} = \dfrac{-49y - 42}{70y + 60} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{8y}{7y + 6} \times \dfrac{10}{10} = \dfrac{80y}{70y + 60} $ Therefore $ q = \dfrac{-49y - 42}{70y + 60} - \dfrac{80y}{70y + 60} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-49y - 42 - 80y }{70y + 60} $ Distribute the negative sign: $q = \dfrac{-49y - 42 - 80y}{70y + 60}$ $q = \dfrac{-129y - 42}{70y + 60}$